Model Approximation for Discrete-Time State-Delay Systems in the T-S Fuzzy Framework

作者：Wu, Ligang^*; Su, Xiaojie; Shi, Peng; Qiu, Jianbin

来源：IEEE Transactions on Fuzzy Systems, 2011, 19(2): 366-378.

DOI：10.1109/TFUZZ.2011.2104363

• Delay partitioning
• discrete-time systems
• H-infinity model approximation
• Takagi-Sugeno (T-S) fuzzy systems
• time delay

This paper is concerned with the problem of H-infinity model approximation for discrete-time Takagi-Sugeno (T-S) fuzzy time-delay systems. For a given stable T-S fuzzy system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well in an H-infinity performance but is also translated into a linear lower dimensional system. By applying the delay partitioning approach, a delay-dependent sufficient condition is proposed for the asymptotic stability with an H-infinity error performance for the error system. Then, the H-infinity model approximation problem is solved by using the projection approach, which casts the model approximation into a sequential minimization problem subject to linear matrix inequality (LMI) constraints by employing the cone complementary linearization algorithm. Moreover, by further extending the results, H-infinity model approximation with special structures is obtained, i.e., delay-free model and zero-order model. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

• 出版日期2011-4
• 单位哈尔滨工业大学